Math Manipulatives

During the first decade of the twentieth century, American mathematics educators adopted and implemented three major methodologies regarding teaching mathematics: the drill and practice approach (19201930), the meaningful arithmetic approach (19301960), and the new mathematics approach (19601970)...Most mathematics educators believe that this nation is experiencing the fourth major phase in mathematics education in this century, one initiated by the publication of the Curriculum and Evaluation Standards for School Mathematics of the National Council of Teachers of Mathematics...(p. 2650)

The shift to which Terry (1995) refers is instructional in nature and refers to a movement away from pencil and paper computation towards utilizing problem-solving techniques to focus on mental mathematics. The basic assumption of this approach is that what is important in acquisition is not merely learning calculation but rather obtaining an understanding of mathematical concepts and the ability to engage in mathematical thought. A substantial portion of the many methods educators use in this new perspective (e.g., the use of story/literature, Peg Boards, Logic Blocks, etc.) consists of manipulatives which Terry defines as concrete objects that allow for mathematical problem solving.

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tion skills and spatial sense. Study participants were divided into three conditions: (1) the Mathematics Manipulative condition (MM); (2) the Mathematics Manipulative Software (MS) condition; and (3) the Mathematics Manipulative with Mathematics Manipulative Software (BOTH). Students in each group received three weeks of training. The focus of all training was upon the development of computation skills. The specific focus of grades two and three was upon addition while the specific focus for grades four and five was upon multiplication. In addition, a one week unit was taught which focused on the development of spatial sense operationally defined as the ability of the subjects to create layering models. Base Ten Blocks and attribute shapes, both in manipulative and manipulative software form, were utilized for the computation unit and spatial sense unit, respectively. Data were analyzed using a series of analyses of variance. Findings revealed that groups differed in terms of learning computational skills but not in terms of improving their spatial sense perceptions. Computational skills were found to be highest in the BOTH condition. However, teachers preferred the computer software condition rather than the r
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